We investigate experimentally and theoretically the evolution of Ne2+ ion momentum distributions from Nonsequential Double Ionization (NSDI) in few-cycle laser pulses with respect to the Carrier Envelope Phase (CEP). The distributions depend strongly on the CEP and exhibit an asymmetric double-hump structure at some CEPs. A semiclassical calculation can reproduce the experimental observations qualitatively, where the rescattering scenario is identified as the main mechanism of double ionization. Analysis based on this semiclassical model reveals that double ionization happens a little later than the collision. Depending on the time difference between the ionization moment and the collision moment, we can distinguish two ionization pathways involved, i.e., Recollision Impact Ionization (RII) (with time difference below 0.1 optical cycle) and Recollision-Excitation and Subsequent Ionization (RESI) (with time difference above 0.1 optical cycle) pathways. The asymmetric pattern results from both RII and RESI: RII leads to the asymmetric double-hump structure, while RESI contributes to the low momentum part and makes the dip of the double-hump structure shallower. Furthermore, Ne2+ ion momentum distributions from RII depend strongly on the CEP and the distributions from RESI seem to be not very sensitive to the CEP. To shed more light on physical mechanism of the asymmetric momentum distribution, the momentum distributions from two ionized electrons are presented at the collision moment, the ionization moment and the moment right after laser field ends for each pathway, respectively. The comparison unravels that the asymmetry comes from the asymmetric acceleration from the laser electric field after the double ionization moments. To demonstrate the significant role of long range Coulomb potential in NSDI process, we replace the Coulomb potential with a short-range model potential in the calculation and the results show appreciable distinctions from the case of Coulomb potential. It is clarified that the Coulomb potential raises the yields of RESI process, which, in turn, makes the dip shallower.